Maximum - practice problems
The maximum is the largest value in a set of numbers or the highest point on a function within a given domain. In calculus, local maxima occur where a function changes from increasing to decreasing, identified by finding where the derivative equals zero and using the second derivative test. Global maxima represent the absolute highest value over the entire domain. Maximum problems are central to optimization, where constraints are used to find the best possible outcome. Applications include maximizing profit, minimizing cost, finding optimal dimensions, and determining extreme values in physics and engineering. Understanding maxima requires knowledge of functions, derivatives, and critical point analysis.Instructions: Take your time with each problem and write out how you solved it step by step.
Number of problems found: 180
- The perimeter 13
The perimeter of a rectangle is 22cm. What are its dimensions if it has a maximum area? - Four plates
Four equal maximum sized circular plates are cut off from a square paper sheet of area 784 sq cm. Calculate the circumference of each plates. - Minimum interior angle
What is the minimum interior angle possible for a regular polygon? - Product - maximum
If x+y is 12 then what is the maximum value of x×y? - Soil erosion
From 1842 to 1875, the yearly erosion of 61/100 meters to a maximum of 1 17/50 meters. By how much did these rates of erosion differ? - Latanya
Latanya plans to repaint some classroom bookcases. She has 5 3/5 gallons of paint. All bookcases are the same size, and each requires 1/2 gallon of paint. What is the maximum number of complete bookcases she can paint? - The following 4
The following are the scores of 10 students in a quiz in Teaching Mathematics in the Intermediate Grades subject: 14, 16, 13, 17, 16, 16, 13, 19, 17, and 13. Find the mode and interpret it - Min-max
What is the maximum and minimum of the data set: 6, 2, 3, 3, 2, 2 - A plumber 3
A plumber can buy plastic pipes in 6-foot and 12-foot lengths. The current job requires eight 4-foot lengths, five 5-foot lengths, and three 7-foot lengths. The plumber wants to figure out how many of each of the two stock lengths should be bought to mini - Dogde Caliber
The petrol kilometers M (unit: kilometers per liter) of the Dodge Caliber car is modeled by the function: M(s) = - 1/28s² + 3s- 31 What is the car's best petrol kilometers, and what speed is attained? - In a football
In a football tournament of eight teams, where each team played each other exactly once, points were awarded as follows: the winner of the match received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the - Cinema visitors
There are 35 seats in each row of an open-air cinema. Determine the maximum number of visitors that can fit in the viewing area, if we know that there are more than 705 and less than 740. - Hockey - game
A hockey goalkeeper has a save success rate of 93.5%. What is the probability that he will keep a clean sheet in a match when facing 25 shots? What is the probability that he will concede a maximum of 2 goals? - Isosceles
A flower bed has the shape of an isosceles triangle with a base of 25m and sides of 30m. Calculate the maximum number of flowers that can be planted in this bed, assuming that one flower requires about 8 dm² of square area. Round the result to the nearest - Frames
A framer is to prepare 23 picture frames. The frame will have dimensions of 30 cm and 42 cm. The strips from which he will make the frames are 3 meters long. a) How many frames will he make from one strip? b) How many strips will he need? - Wrench Lever Force
The key works like a lever, where one arm is the radius of the bolt, and the other is the length of the key. If key no. 12 (for screws with a diameter of 12 mm) and a length of 12 cm can be tightened with a maximum force of 100 N, what force does the wren - Cylindrical bucket
The cylindrical bucket was filled 2/3 with water. You know that the diameter of the bottom is 25 cm, and the water reaches a height of 24 cm. What is the maximum amount of water that can be poured into the bucket? - Pool inflow half
The pool has a maximum water capacity of 1200 hl. How many hours will the pool be half complete if the first inflow is 200 l per minute and the second 100 l per minute? - Concorde weight reserve
The maximum take-off weight of the Concorde aircraft is 185,000 kg. What reserve does it have for fuel, passengers, and their luggage if the plane's weight is 78,900 kg? - Tram - safe downhill
What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15.
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